Problem: Simplify the following expression: $z = \dfrac{y^2 - 11y + 18}{y - 2} $
Solution: First factor the polynomial in the numerator. $ y^2 - 11y + 18 = (y - 2)(y - 9) $ So we can rewrite the expression as: $z = \dfrac{(y - 2)(y - 9)}{y - 2} $ We can divide the numerator and denominator by $(y - 2)$ on condition that $y \neq 2$ Therefore $z = y - 9; y \neq 2$